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Peer-reviewedCC BY 4.0Mathematics

Combined Influence of Membrane Profiling and Wing-Shaped Spacers on Ion Transport: A Two-Dimensional Potentiodynamic Study

  • Anna Ovsyannikova1
  • Evgenia Kirillova2
  • Anna Kovalenko3
  • Anastasiia Lelekova4
  • Alexandra Ovsyannikova4
  • Makhamet Urtenov3
4 affiliations
  1. 1Faculty of Information Technology and Big Data Analysis, Financial University under the Government of the Russian Federation, 125167 Moscow, Russia
  2. 2Faculty of Architecture and Civil Engineering, RheinMain University of Applied Sciences and Arts, 65197 Wiesbaden, Germany
  3. 3Faculty of Computer Technologies and Applied Mathematics, Kuban State University, 350040 Krasnodar, Russia
  4. 4School of Software Engineering, Faculty of Computer Science, HSE University, 109028 Moscow, Russia
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Abstract

Membrane profiling and near-membrane spacers modify concentration polarization by altering fluid flow and the membrane–solution interface. This study examines their combined influence using a two-dimensional Nernst–Planck–Poisson–Navier–Stokes model with a voltage ramp of 5 mV/s. The geometries comprise a smooth membrane without spacers, a profiled membrane without spacers, and six wing arrangements adjacent to a profiled membrane. The feed concentration is 0.01 mol/m3, the protrusion radius is 0.5 mm, and the center-to-center pitch is 1.5 mm. Current data from five identifiable model files are compared over a common interval up to 1.2 V using a dimensionless domain-integrated current. Wing placement affects the current response, while profiling increases the geometric membrane contour by 28.54%. An analytical reference limiting current is calculated using the Levêque equation. The comparison with published three-dimensional results provides qualitative support for the transport mechanism. Systematic numerical uncertainty assessment, quantitative three-dimensional validation, geometry optimization, and energy comparisons at equal salt removal are identified as further research beyond the scope of the present study.

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Cite

BibTeXRIS
BibTeX
@article{ovsyannikova2026combined,
  title = {{Combined Influence of Membrane Profiling and Wing-Shaped Spacers on Ion Transport: A Two-Dimensional Potentiodynamic Study}},
  author = {Anna Ovsyannikova and Evgenia Kirillova and Anna Kovalenko and Anastasiia Lelekova and Alexandra Ovsyannikova and Makhamet Urtenov},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203825},
  url = {https://www.mdpi.com/2227-7390/14/20/3825},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Combined Influence of Membrane Profiling and Wing-Shaped Spacers on Ion Transport: A Two-Dimensional Potentiodynamic Study
AU  - Anna Ovsyannikova
AU  - Evgenia Kirillova
AU  - Anna Kovalenko
AU  - Anastasiia Lelekova
AU  - Alexandra Ovsyannikova
AU  - Makhamet Urtenov
PY  - 2026
DA  - 2026/10/21
JO  - Mathematics
DO  - 10.3390/math14203825
UR  - https://www.mdpi.com/2227-7390/14/20/3825
AB  - Membrane profiling and near-membrane spacers modify concentration polarization by altering fluid flow and the membrane–solution interface. This study examines their combined influence using a two-dimensional Nernst–Planck–Poisson–Navier–Stokes model with a voltage ramp of 5 mV/s. The geometries comprise a smooth membrane without spacers, a profiled membrane without spacers, and six wing arrangements adjacent to a profiled membrane. The feed concentration is 0.01 mol/m3, the protrusion radius is 0.5 mm, and the center-to-center pitch is 1.5 mm. Current data from five identifiable model files are compared over a common interval up to 1.2 V using a dimensionless domain-integrated current. Wing placement affects the current response, while profiling increases the geometric membrane contour by 28.54%. An analytical reference limiting current is calculated using the Levêque equation. The comparison with published three-dimensional results provides qualitative support for the transport mechanism. Systematic numerical uncertainty assessment, quantitative three-dimensional validation, geometry optimization, and energy comparisons at equal salt removal are identified as further research beyond the scope of the present study.
SN  - 2227-7390
ER  -